[jeffpea]

Nevadaref -- Using your logic, if the same scenario occurred after time expired in the 4th quarter and the officials did the same thing (mistakenly administered the technical FT's before the 1 minute "intermission" prior to the beginning of overtime), would the made FT's count towards the score in the 4th quarter? Of course not. Those points would count towards the overtime period. The officials would still administer the throw-in penalty to start the over-time period.
The only situation that applies, using your thought process, is if you had a foul on a shot that was released before the clock expired at the end of the quarter and needed to shoot FT's. Then you have a T before you administer the FT's (remember the quarter has not ended until all FT's or penalties are administered). You would shoot the common foul FT(s), then the T FT's. The quarter has then ended and you cannot carry the throw-in penalty to the next period, so you go to AP arrow.
Does that make sense to you?